Impulses efficiently propagate into nominally dry granular beds and backscatter from buried inclusions in such beds may be potentially exploited to image shallow buried objects (SBOs). However, reliable imaging of SBOs requires “cleaning up” of surface vibrations, and, in addition to three-dimensional (3D) particle dynamics simulations, a phenomenological model to parametrize the bed surface may be useful for field applications. We introduce a 1D mean-field-like toy model with two parameters, which allows one to model surface vibrations, is consistent with experiments in a granular bed, and can help estimate the approximate signal transmission properties of the bed. © 2003 The American Physical Society.